7 comments:

Major Ursa
said...

"he’s created an unrealistic but intriguing mathematical model quite divorced from biological evolution in the real world"

I agree with you, so if the following sounds like a defense of Chaitin's work, it's not meant to be. I just have a different way of understanding one thing he wrote. He wrote “conventional biologists ... suspect that life on Earth was either seeded by accident ... or deliberately planted.” My first instinct was not to read "seeded" literally. In my less-than-literal reading, I figured that even a lightning strike on a murky pond counts as "seeding." I simply read him as saying that life on Earth is ultimately an accident. Any chance that's an accurate interpretation?

Also, you wrote: "But if it is supposed to be relevant to biological evolution, there are a numberof obvious objections." May I add an objection to your well-thought-out ones? Chaitin writes: "If I-prime is bigger than I, the new program P-prime is deemed to be more fit; P is then killed off and P-prime replaces it." Well, does that killing-off always happen in real life? Sometimes, the less fit creature lives on. It might even be more fit, but in a different but important way, than the over-all- more fit creature. If this weren't true, then we'd never hear that silly argument, "if humans evolved from chimpanzees, then why are there still chimpanzees?!"

There is a common failure mode that occurs to scientists (probably not just scientists, but that's what I'm most familiar with) who have made at least one or two significant contributions to their field. All too many of them somehow get the impression that every random thought that subsequently appears in their head is more likely to be correct and important than anyone else's random thoughts.

How this affects said scientist depends on a number of factors. In its most benign form, it means that the scientist can get low-value material published in quantities which a less-famous person could not get away with (e.g. Rob Pike). A more typical moderate case is serial public foolishness (e.g. James Watson). In its most malignant form, it can mean outright crankery (e.g. Brian Josephson).

I'll leave the reader to judge where Lynn Margulis lies on the spectrum.

Some scientists manage to avoid this. Some do it by avoiding success at all costs. Some just have the right kind of personality to keep their egos in check.

I should add that I used to be a compiler writer. For me, Chaitin will always be the graph colouring register allocation guy. That work will live on for a very long time.

I’m trying to create a new field, and I’d like to invite you all to leap in, join [me] if you feel like it. I think we have a remarkable opportunity to create a kind of a theoretical mathematical biology…

So let me tell you a little bit about this viewpoint … of biology which I think may enable us to create a new … mathematical version of Darwin’s theory, maybe even prove that evolution works for the skeptics who don’t believe it…

I don’t want evolution to stagnate, because as a pure mathematician, if the system evolves and it stops evolving, that’s like it never evolved at all… I want to prove that evolution can go on forever…

OK, so software is everywhere there, and what I want to do is make a theory about randomly evolving, mutating and evolving software – a little toy model of evolution where I can prove theorems, because I love Darwin’s theory, I have nothing against it, but, you know, it’s just an empirical theory. As a pure mathematician, that’s not good enough…

… John Maynard Smith is saying that we define life as something that evolves according to Darwin’s theory of evolution. Now this may seem that it’s totally circular reasoning, but it’s not. It’s not that kind of reasoning, because the whole point, as a pure mathematician, is to prove that there is something in the world of pure math that satisfies this definition – you know, to invent a mathematical life-form in the Pythagorean world that I can prove actually does evolve according to Darwin’s theory, and to prove that there is something which satisfies this definition of being alive. And that will be at least a proof that in some toy model, Darwin’s theory of evolution works – which I regard as the first step in developing this as a theory, this viewpoint of life as evolving software….

…I want to know what is the simplest thing I need mathematically to show that evolution by natural selection works on it? You see, so this will be the simplest possible life form that I can come up with….

The first thing I … want to see is: how fast will this system evolve? How big will the fitness be? How big will the number be that these organisms name? How quickly will they name the really big numbers? So how can we measure the rate of evolutionary progress, or mathematical creativity of my little mathematicians, these programs? Well, the way to measure the rate of progress, or creativity, in this model, is to define a thing called the Busy Beaver function. One way to define it is the largest fitness of any program of N bits in size. It’s the biggest whole number without a sign that can be calculated if you could name it, with a program of N bits in size….

So what happens if we do that, which is sort of cumulative random evolution, the real thing? Well, here’s the result. You’re going to reach Busy Beaver function N in a time that is – you can estimate it to be between order of N squared and order of N cubed. Actually this is an upper bound. I don’t have a lower bound on this. This is a piece of research which I would like to see somebody do – or myself for that matter – but for now it’s just an upper bound. OK, so what does this mean? This means, I will put it this way. I was very pleased initially with this.

Table:Exhaustive search reaches fitness BB(N) in time 2^N.Intelligent Design reaches fitness BB(N) in time N. (That’s the fastest possible regime.)Random evolution reaches fitness BB(N) in time between N^2 and N^3.

This means that picking the mutations at random is almost as good as picking them the best possible way…

But I told a friend of mine … about this result. He doesn’t like Darwinian evolution, and he told me, “Well, you can look at this the other way if you want. This is actually much too slow to justify Darwinian evolution on planet Earth. And if you think about it, he’s right… If you make an estimate, the human genome is something on the order of a gigabyte of bits. So it’s … let’s say a billion bits – actually 6 x 10^9 bits, I think it is, roughly – … so we’re looking at programs up to about that size [here he points to N^2 on the slide] in bits, and N is about of the order of a billion, 10^9, and the time, he said … that’s a very big number, and you would need this to be linear, for this to have happened on planet Earth, because if you take something of the order of 10^9 and you square it or you cube it, well … forget it. There isn’t enough time in the history of the Earth … Even though it’s fast theoretically, it’s too slow to work. He said, “You really need something more or less linear.” And he has a point…